A generic 3-dimensional system to mimic trabecular bone surface adaptation

The paper presents the structure optimizing system based on surface remodelling. The grounds for algorithm formulation are given by the bone remodelling phenomenon leading to optimization of trabecular network in the bone. The assumptions, algorithms and limitations of the own mesh generator Cosmoprojector are described. Unlike other approaches, the system is able to mimic real bone evolution including tissue consolidation and separation. The article presents a closed system consisting of finite element mesh generation, decision criteria for structure adaptation and finite element analysis in parallel environment. It also provides some computation results obtained by using specially designed software.     

Correlation between pre-operative periprosthetic bone density and post-operative bone loss in THA can be explained by strain-adaptive remodelling.

Periprosthetic adaptive bone remodelling after total hip arthroplasty can be simulated in computer models, combining bone remodelling theory with finite element analysis. Patient specific three-dimensional finite element models of retrieved bone specimens from an earlier bone densitometry (DEXA) study were constructed and bone remodelling simulations performed. Results of the simulations were analysed both qualitatively and quantitatively. Patterns of predicted bone loss corresponded very well with the DEXA measurements on the retrievals. The amount of predicted bone loss, measured quantitatively by simulating DEXA on finite element models, was found to be inversely correlated with the initial bone mineral content. It was concluded that the same clinically observed correlation can therefore be explained by mechanically induced remodelling. This finding extends the applicability of numerical pre-clinical testing to the analysis of interaction between implant design and initial state of the bone.     

Prediction of bone adaptation in the ulnar-osteotomized sheep's forelimb using an anatomical finite element model

A method for the prediction of the time-course of bone adaptation based on an alternative hypothesis of strength optimization has been previously investigated and developed by Prendergast and Taylor¹. This paper extends our work in the study of the effectiveness of this bone adaptation model in predicting similar bone remodelling to that observed in animal experiments. In particular the experimental work which has been modelled is that of Lanyon, Goodship, Pye and McFie². An anatomical finite element model of the sheep's forelimb has been generated for this purpose and is used to estimate stresses in the bone structure for the normal and osteotomized condition. The propensity for remodelling of the altered bone structure is predicted using the proposed remodelling law for the new stress field in the bone structure. The preliminary results indicate an initial bone adaptation pattern similar to that observed experimentally without the necessity to use arbitrarily different constants for the endosteal and periosteal surfaces. We therefore suggest that the remodelling law based on damage and repair gives a better predictive model of bone adaptation than previous models.     

Computational simulation of internal bone remodelling around dental implants: a sensitivity analysis

This study aimed to predict the distribution of bone trabeculae, as a density change per unit time, around a dental implant based on applying a selected mathematical remodelling model. The apparent bone density change as a function of the mechanical stimulus was the base of the applied remodelling model that describes disuse and overload bone resorption. The simulation was tested in a finite element model of a screw-shaped dental implant in an idealised bone segment. The sensitivity of the simulation to different mechanical parameters was investigated; these included element edge length, boundary conditions, as well as direction and magnitude of the implant loads. The alteration in the mechanical parameters had a significant influence on density distribution and model stability, in particular at the cortical bone region. The remodelling model could succeed to achieve trabeculae-like structure around osseointegrated dental implants. The validation of this model to a real clinical case is required.     

Subject-specific bone remodelling of the scapula

Finite element analyses, with increasing levels of detail and complexity, are becoming effective tools to evaluate the performance of joint replacement prostheses and to predict the behaviour of bone. As a first step towards the study of the complications of shoulder arthroplasty, the aim of this work was the development and validation of a 3D finite element model of an intact scapula for the prediction of the bone remodelling process based on a previously published model that attempts to follow Wolff's law. The boundary conditions applied include full muscle and joint loads taken from a multibody system of the upper limb based on the same subject whose scapula was here analysed. To validate the bone remodelling simulations, qualitative and quantitative comparisons between the predicted and the specimen's bone density distribution were performed. The results showed that the bone remodelling model was able to successfully reproduce the actual bone density distribution of the analysed scapula.     

Computational simulation of internal bone remodelling around dental implants: a sensitivity analysis

This study aimed to predict the distribution of bone trabeculae, as a density change per unit time, around a dental implant based on applying a selected mathematical remodelling model. The apparent bone density change as a function of the mechanical stimulus was the base of the applied remodelling model that describes disuse and overload bone resorption. The simulation was tested in a finite element model of a screw-shaped dental implant in an idealised bone segment. The sensitivity of the simulation to different mechanical parameters was investigated; these included element edge length, boundary conditions, as well as direction and magnitude of the implant loads. The alteration in the mechanical parameters had a significant influence on density distribution and model stability, in particular at the cortical bone region. The remodelling model could succeed to achieve trabeculae-like structure around osseointegrated dental implants. The validation of this model to a real clinical case is required.     

A contact model with ingrowth control for bone remodelling around cementless stems.

This work presents a computational model for bone remodelling around cementless stems. The problem is formulated as a material optimisation problem considering the bone and stem surfaces to be in contact. To emphasise the behaviour of the bone/stem interface, the computer model detects the existence of bone ingrowth during the remodelling; consequently, the contact conditions are changed for a better interface simulation. The trabecular bone is modelled as a strictly orthotropic material with equivalent properties computed by homogenisation. The distribution of bone relative density is obtained by the minimisation of a function that considers both the bone structural stiffness and the biological cost associated with metabolic maintenance of bone tissue. The situation of multiple load conditions is considered. The remodelling law, obtained from the necessary conditions for an optimum, is derived analytically from the optimisation problem and solved numerically using a suitable finite element mesh. The formulation is applied to an implanted femur. Results of bone density and ingrowth distribution are obtained for different coating conditions. Bone ingrowth does not occur over the entire coated surfaces. Indeed, we observed regions where separation or high relative displacement occurs that preclude bone ingrowth attachment. This prediction of the model is consistent with clinical observations of bone ingrowth. Thus, this model, which detect bone ingrowth and allow modification of the interface conditions, are useful for analysis of existing stems as well as design optimisation of coating extent and location on such stems.     

Trabecular bone fracture healing simulation with finite element analysis and fuzzy logic

Trabecular bone fractures heal through intramembraneous ossification. This process differs from diaphyseal fracture healing in that the trabecular marrow provides a rich vascular supply to the healing bone, there is very little callus formation, woven bone forms directly without a cartilage intermediary, and the woven bone is remodelled to form trabecular bone. Previous studies have used numerical methods to simulate diaphyseal fracture healing or bone remodelling, however not trabecular fracture healing, which involves both tissue differentiation and trabecular formation. The objective of this study was to determine if intramembraneous bone formation and remodelling during trabecular bone fracture healing could be simulated using the same mechanobiological principles as those proposed for diaphyseal fracture healing. Using finite element analysis and the fuzzy logic for diaphyseal healing, the model simulated formation of woven bone in the fracture gap and subsequent remodelling of the bone to form trabecular bone. We also demonstrated that the trabecular structure is dependent on the applied loading conditions. A single model that can simulate bone healing and remodelling may prove to be a useful tool in predicting musculoskeletal tissue differentiation in different vascular and mechanical environments.     

Finite element analysis of bone remodelling with piezoelectric effects using an open-source framework

Bone tissue exhibits piezoelectric properties and thus is capable of transforming mechanical stress into electrical potential. Piezoelectricity has been shown to play a vital role in bone adaptation and remodelling processes. Therefore, to better understand the interplay between mechanical and electrical stimulation during these processes, strain-adaptive bone remodelling models without and with considering the piezoelectric effect were simulated using the Python-based open-source software framework. To discretise numerical attributes, the finite element method (FEM) was used for the spatial variables and an explicit Euler scheme for the temporal derivatives. The predicted bone apparent density distributions were qualitatively and quantitatively evaluated against the radiographic scan of a human proximal femur and the bone apparent density calculated using a bone mineral density (BMD) calibration phantom, respectively. Additionally, the effect of the initial bone density on the resulting predicted density distribution was investigated globally and locally. The simulation results showed that the electrically stimulated bone surface enhanced bone deposition and these are in good agreement with previous findings from the literature. Moreover, mechanical stimuli due to daily physical activities could be supported by therapeutic electrical stimulation to reduce bone loss in case of physical impairment or osteoporosis. The bone remodelling algorithm implemented using an open-source software framework facilitates easy accessibility and reproducibility of finite element analysis made.

     

Comparative analysis of bone remodelling models with respect to computerised tomography-based finite element models of bone

Subject-specific finite element models are an extensively used tool for the numerical analysis of the biomechanical behaviour of human bones. However, bone modelling is not an easy task due to the complex behaviour of bone tissue, involving non-homogeneous and anisotropic mechanical properties. Moreover, bone is a living tissue and therefore its microstructure and mechanical properties evolve with time in a known process called bone remodelling. This phenomenon has been widely studied, many being the numerical models that have been formulated to predict density distribution and its evolution in several bones. The aim of the present study is to assess the capability of a bone remodelling model to predict the bone density distribution of different types of human bone (femur, tibia and mandible) comparing the obtained results with the bone density estimated by means of computerised tomography. Good accuracy was observed for the bone remodelling predictions including the thickness of the cortical layer.     

Interstitial fluid flow in the osteon with spatial gradients of mechanical properties: a finite element study

Bone remodelling is the process that maintains bone structure and strength through adaptation of bone tissue mechanical properties to applied loads. Bone can be modelled as a porous deformable material whose pores are filled with cells, organic material and interstitial fluid. Fluid flow is believed to play a role in the mechanotransduction of signals for bone remodelling. In this work, an osteon, the elementary unit of cortical bone, is idealized as a hollow cylinder made of a deformable porous matrix saturated with an interstitial fluid. We use Biot’s poroelasticity theory to model the mechanical behaviour of bone tissue taking into account transverse isotropic mechanical properties. A finite element poroelastic model is developed in the COMSOL Multiphysics software. Elasticity equations and Darcy’s law are implemented in this software; they are coupled through the introduction of an interaction term to obtain poroelasticity equations. Using numerical simulations, the investigation of the effect of spatial gradients of permeability or Poisson’s ratio is performed. Results are discussed for their implication on fluid flow in osteons: (i) a permeability gradient affects more the fluid pressure than the velocity profile; (ii) focusing on the fluid flow, the key element of loading is the strain rate; (iii) a Poisson’s ratio gradient affects both fluid pressure and fluid velocity. The influence of textural and mechanical properties of bone on mechanotransduction signals for bone remodelling is also discussed.     

A Comparative Analysis of Different Treatments for Distal Femur Fractures using the Finite Element Method

The main objective of this work is the evaluation, by means of the finite element method (FEM) of the mechanical stability and long-term microstructural modifications in bone induced to three different kinds of fractures of the distal femur by three types of implants: the Condyle Plate, the less invasive stabilization system plate (LISS) and the distal femur nail (DFN). The displacement and the stress distributions both in bone and implants and the internal bone remodelling process after fracture and fixation are obtained and analysed by computational simulation. The main conclusions of this work are that distal femoral fractures can be treated correctly with the Condyle Plate, the LISS plate and the DFN. The stresses both in LISS and DFN implant are high especially around the screws. When respect to remodelling, the LISS produces an important resorption in the fractured region, while the other two implants do not strongly modify bone tissue microstructure.     

Multiscale methodology for bone remodelling simulation using coupled finite element and neural network computation

The aim of this paper is to develop a multiscale hierarchical hybrid model based on finite element analysis and neural network computation to link mesoscopic scale (trabecular network level) and macroscopic (whole bone level) to simulate the process of bone remodelling. As whole bone simulation, including the 3D reconstruction of trabecular level bone, is time consuming, finite element calculation is only performed at the macroscopic level, whilst trained neural networks are employed as numerical substitutes for the finite element code needed for the mesoscale prediction. The bone mechanical properties are updated at the macroscopic scale depending on the morphological and mechanical adaptation at the mesoscopic scale computed by the trained neural network. The digital image-based modelling technique using μ-CT and voxel finite element analysis is used to capture volume elements representativeof 2 mm³ at the mesoscale level of the femoral head. The input data for the artificial neural network are a set of bone material parameters, boundary conditions and the applied stress. The output data are the updated bone properties and some trabecular bone factors. The current approach is the first model, to our knowledge, that incorporates both finite element analysis and neural network computation to rapidly simulate multilevel bone adaptation.     

A comparative analysis of different treatments for distal femur fractures using the finite element method

The main objective of this work is the evaluation, by means of the finite element method (FEM) of the mechanical stability and long-term microstructural modifications in bone induced to three different kinds of fractures of the distal femur by three types of implants: the Condyle Plate, the less invasive stabilization system plate (LISS) and the distal femur nail (DFN). The displacement and the stress distributions both in bone and implants and the internal bone remodelling process after fracture and fixation are obtained and analysed by computational simulation. The main conclusions of this work are that distal femoral fractures can be treated correctly with the Condyle Plate, the LISS plate and the DFN. The stresses both in LISS and DFN implant are high especially around the screws. When respect to remodelling, the LISS produces an important resorption in the fractured region, while the other two implants do not strongly modify bone tissue microstructure.     

Numerical simulation of load-induced bone structural remodelling using stress-limit criterion

A simple and efficient numerical method for predicting the remodelling of adaptive materials and structures under applied loading was presented and implemented within a finite element framework. The model uses the trajectorial architecture theory of optimisation to predict the remodelling of material microstructure and structural organisation under mechanical loading. We used the proposed model to calculate the density distribution of proximal femur in the frontal plane. The loading considered was the hip joint contact forces and muscular forces at the attachment sites of the muscles to the bone. These forces were estimated from a separate finite element calculation using a heterogeneous three-dimensional model of the proximal femur. The density distributions obtained by this procedure has a qualitative similarity with in vivo observations. Solutions displayed the characteristic high-density channels that are evident in the Dual X-ray Absorptiometry scan. There is also evidence of the intramedullary canal, as well as low-density regions in the femoral neck. Several parametric studies were carried out to highlight the advantages of the proposed method, which includes fast convergence and low-computational cost. The potential applications of the proposed method in predicting bone structural remodelling in cancer are also briefly discussed.     

Simulating localised cellular inflammation and substrate properties in a strain energy density based bone remodelling algorithm for use in modelling trauma

Bone responds to mechanical stimulus and a range of pre-existing finite element models have been suggested to reproduce the internal physiological structure of bone. Inflammation effects are not included in these models, yet inflammation is a key component of bone repair in trauma. Therefore, a model is proposed and tested here that extends these methods to include parameters that could be considered to represent the behaviour of bone remodelling when influenced by inflammation. The proposed model regulates remodelling based on findings from recent studies into the nature of heterotopic ossification, the formation of heterotopic bone, which have revealed information about the nature of bone after high levels of trauma. These parameters include consideration of the distance from the zone of trauma, the density of mesenchymal stem cells, and substrate stiffness as a trigger for cells becoming osteogenic. The method is tested on a two-dimensional plate model and shows that the new extended algorithm can produce a range of structures depending on inputs that could be used in the future to replicate physiological scenarios.     

Numerical simulation of the remodelling process of trabecular architecture around dental implants

Dental implants may alter the mechanical environment in the jawbone, thereby causing remodelling and adaptation of the surrounding trabecular bone tissues. To improve the efficacy of dental implant systems, it is necessary to consider the effect of bone remodelling on the performance of the prosthetic systems. In this study, finite element simulations were implemented to predict the evolution of microarchitecture around four implant systems using a previously developed model that combines both adaptive and microdamage-based mechano-sensory mechanisms in bone remodelling process. Changes in the trabecular architecture around dental implants were mainly focused. The simulation results indicate that the orientational and ladder-like architecture around the implants predicted herein is in good agreement with those observed in animal experiments and clinical observations. The proposed algorithms were shown to be effective in simulating the remodelling process of trabecular architecture around dental implant systems. In addition, the architectural features around four typical dental implant systems in alveolar bone were evaluated comparatively.     

A Bone-remodelling Scheme Based on Principal Strains Applied to a Tooth During Translation

This paper investigates the role of principal strains within the periodontal ligament (PDL) during bone remodelling in orthodontics and particularly in the case of bodily motion (pure translation). Using analytical formulas of stress and strains within the PDL for the particular case of a paraboloidal central incisor during translation, the strains are directly related to the motion of the interface between the alveolar bone and the PDL, called bone surface. It is shown that both normal and shear strains within the PDL are of the same importance for bone surface motion. Moreover, both “mean average” and “geometrical average” of principal strains within the PDL play a significant role in the bone remodelling process, as they contribute with the same proportionality. In summary, the proposed formulas differ than previous ones that had been successfully applied to describe remodelling within long bones. The proposed theory is also sustained by a linear finite element analysis.     

Bone remodelling analysis of a bovine femur for a veterinary implant design

The response of bovine bone to the presence of an implant is analysed with the aim of simulating bone remodelling in a developing model of a polymeric intramedullary interlocking nail for veterinary use. A 3-D finite element model of the femur diaphysis is built based on computed tomography images and using a CAD-based modelling pipeline. The bone remodelling process after the surgery is analysed and compared with the healthy bone. The remodelling law assumes that bone adapts to the mechanical environment. For the analyses a consistent set of loads is determined for the bovine walk cycle. The remodelling results reproduce the morphologic features of bone and provide evidence of the difference on the bone behaviour when comparing metallic and polymeric nails. Our findings indicate that an intramedullary polymeric nail has the advantage over the metallic one of improving long-term bone healing and possibly avoiding the need of the implant removal.     

A bone-remodelling scheme based on principal strains applied to a tooth during translation

This paper investigates the role of principal strains within the periodontal ligament (PDL) during bone remodelling in orthodontics and particularly in the case of bodily motion (pure translation). Using analytical formulas of stress and strains within the PDL for the particular case of a paraboloidal central incisor during translation, the strains are directly related to the motion of the interface between the alveolar bone and the PDL, called bone surface. It is shown that both normal and shear strains within the PDL are of the same importance for bone surface motion. Moreover, both "mean average" and "geometrical average" of principal strains within the PDL play a significant role in the bone remodelling process, as they contribute with the same proportionality. In summary, the proposed formulas differ than previous ones that had been successfully applied to describe remodelling within long bones. The proposed theory is also sustained by a linear finite element analysis.